When does the H_infinity fixed-lag smoothing performance saturate?

L. Mirkin and G. Meinsma
Abstract
A notable difference between the $H_2$ and $H_infty$ smoothing is that the
achievable performance in the latter problem might ``saturate'' as the
function of the smoothing lag in the sense that there might exist a finite
smoothing lag for which the achievable performance level is the same as for
the infinite smoothing lag. In this paper necessary and sufficient conditions
under which such a saturation takes place are derived. In particular, it is
shown that the $H_\infty$ performance saturates only if the $H_infty$
norm of the
optimal error system is achieved at the infinite frequency, i.e., if the
worst case disturbance is ``infinitely fast'' and thus in a sense
unpredictable.